tan-example (used to crash)

Percentage Accurate: 79.1% → 99.7%

Time: 52.4s

Alternatives: 18

Speedup: 1.0×

Specification

\[\left(\left(\left(x = 0 \lor 0.5884142 \leq x \land x \leq 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \leq y \land y \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq y \land y \leq 1.751224 \cdot 10^{+308}\right)\right) \land \left(-1.776707 \cdot 10^{+308} \leq z \land z \leq -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \leq z \land z \leq 1.725154 \cdot 10^{+308}\right)\right) \land \left(-1.796658 \cdot 10^{+308} \leq a \land a \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq a \land a \leq 1.751224 \cdot 10^{+308}\right)\]

Math

\[\begin{array}{l} \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\frac{1}{\frac{1 - \frac{\tan y \cdot \sin z}{\cos z}}{\tan y + \tan z}} - \tan a\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+
  x
  (-
   (/ 1.0 (/ (- 1.0 (/ (* (tan y) (sin z)) (cos z))) (+ (tan y) (tan z))))
   (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + ((1.0 / ((1.0 - ((tan(y) * sin(z)) / cos(z))) / (tan(y) + tan(z)))) - tan(a));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + ((1.0d0 / ((1.0d0 - ((tan(y) * sin(z)) / cos(z))) / (tan(y) + tan(z)))) - tan(a))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + ((1.0 / ((1.0 - ((Math.tan(y) * Math.sin(z)) / Math.cos(z))) / (Math.tan(y) + Math.tan(z)))) - Math.tan(a));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + ((1.0 / ((1.0 - ((math.tan(y) * math.sin(z)) / math.cos(z))) / (math.tan(y) + math.tan(z)))) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 - Float64(Float64(tan(y) * sin(z)) / cos(z))) / Float64(tan(y) + tan(z)))) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + ((1.0 / ((1.0 - ((tan(y) * sin(z)) / cos(z))) / (tan(y) + tan(z)))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(1.0 / N[(N[(1.0 - N[(N[(N[Tan[y], $MachinePrecision] * N[Sin[z], $MachinePrecision]), $MachinePrecision] / N[Cos[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.2%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. clear-num 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

4. Applied egg-rr 99.7%

   \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]
5. Step-by-step derivation

   1. tan-quot 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \tan y \cdot \color{blue}{\frac{\sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

   2. associate-*r/ 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

6. Applied egg-rr 99.7%

   \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]
7. Add Preprocessing

Alternative 2: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\frac{1}{\frac{1 + \left(-1 - \mathsf{fma}\left(\tan y, \tan z, -1\right)\right)}{\tan y + \tan z}} - \tan a\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+
  x
  (-
   (/ 1.0 (/ (+ 1.0 (- -1.0 (fma (tan y) (tan z) -1.0))) (+ (tan y) (tan z))))
   (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + ((1.0 / ((1.0 + (-1.0 - fma(tan(y), tan(z), -1.0))) / (tan(y) + tan(z)))) - tan(a));
}

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 + Float64(-1.0 - fma(tan(y), tan(z), -1.0))) / Float64(tan(y) + tan(z)))) - tan(a)))
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(1.0 / N[(N[(1.0 + N[(-1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.2%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. clear-num 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

4. Applied egg-rr 99.7%

   \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]
5. Step-by-step derivation

   1. tan-quot 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \tan y \cdot \color{blue}{\frac{\sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

   2. associate-*r/ 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

6. Applied egg-rr 99.7%

   \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]
7. Step-by-step derivation

   1. expm1-log1p-u 90.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\tan y \cdot \sin z}{\cos z}\right)\right)}}{\tan y + \tan z}} - \tan a\right) \]

   2. expm1-undefine 90.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\tan y \cdot \sin z}{\cos z}\right)} - 1\right)}}{\tan y + \tan z}} - \tan a\right) \]

   3. log1p-undefine 90.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(e^{\color{blue}{\log \left(1 + \frac{\tan y \cdot \sin z}{\cos z}\right)}} - 1\right)}{\tan y + \tan z}} - \tan a\right) \]

   4. add-exp-log 99.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(\color{blue}{\left(1 + \frac{\tan y \cdot \sin z}{\cos z}\right)} - 1\right)}{\tan y + \tan z}} - \tan a\right) \]

   5. associate-/l* 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(\left(1 + \color{blue}{\tan y \cdot \frac{\sin z}{\cos z}}\right) - 1\right)}{\tan y + \tan z}} - \tan a\right) \]

   6. tan-quot 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(\left(1 + \tan y \cdot \color{blue}{\tan z}\right) - 1\right)}{\tan y + \tan z}} - \tan a\right) \]

8. Applied egg-rr 99.7%

   \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\left(\left(1 + \tan y \cdot \tan z\right) - 1\right)}}{\tan y + \tan z}} - \tan a\right) \]
9. Step-by-step derivation

   1. associate--l+ 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\left(1 + \left(\tan y \cdot \tan z - 1\right)\right)}}{\tan y + \tan z}} - \tan a\right) \]

   2. fmm-def 99.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(1 + \color{blue}{\mathsf{fma}\left(\tan y, \tan z, -1\right)}\right)}{\tan y + \tan z}} - \tan a\right) \]

   3. metadata-eval 99.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(1 + \mathsf{fma}\left(\tan y, \tan z, \color{blue}{-1}\right)\right)}{\tan y + \tan z}} - \tan a\right) \]

10. Simplified 99.8%

    \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\left(1 + \mathsf{fma}\left(\tan y, \tan z, -1\right)\right)}}{\tan y + \tan z}} - \tan a\right) \]

11. Final simplification 99.8%

    \[\leadsto x + \left(\frac{1}{\frac{1 + \left(-1 - \mathsf{fma}\left(\tan y, \tan z, -1\right)\right)}{\tan y + \tan z}} - \tan a\right) \]
12. Add Preprocessing

Alternative 3: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x - \left(\tan a + \frac{\tan y + \tan z}{\mathsf{fma}\left(\tan y, \tan z, -1\right)}\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (- x (+ (tan a) (/ (+ (tan y) (tan z)) (fma (tan y) (tan z) -1.0)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x - (tan(a) + ((tan(y) + tan(z)) / fma(tan(y), tan(z), -1.0)));
}

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x - Float64(tan(a) + Float64(Float64(tan(y) + tan(z)) / fma(tan(y), tan(z), -1.0))))
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x - N[(N[Tan[a], $MachinePrecision] + N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.2%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. clear-num 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

4. Applied egg-rr 99.7%

   \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]
5. Step-by-step derivation

   1. tan-quot 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \tan y \cdot \color{blue}{\frac{\sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

   2. associate-*r/ 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

6. Applied egg-rr 99.7%

   \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]
7. Step-by-step derivation

   1. expm1-log1p-u 90.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\tan y \cdot \sin z}{\cos z}\right)\right)}}{\tan y + \tan z}} - \tan a\right) \]

   2. expm1-undefine 90.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\tan y \cdot \sin z}{\cos z}\right)} - 1\right)}}{\tan y + \tan z}} - \tan a\right) \]

   3. log1p-undefine 90.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(e^{\color{blue}{\log \left(1 + \frac{\tan y \cdot \sin z}{\cos z}\right)}} - 1\right)}{\tan y + \tan z}} - \tan a\right) \]

   4. add-exp-log 99.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(\color{blue}{\left(1 + \frac{\tan y \cdot \sin z}{\cos z}\right)} - 1\right)}{\tan y + \tan z}} - \tan a\right) \]

   5. associate-/l* 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(\left(1 + \color{blue}{\tan y \cdot \frac{\sin z}{\cos z}}\right) - 1\right)}{\tan y + \tan z}} - \tan a\right) \]

   6. tan-quot 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(\left(1 + \tan y \cdot \color{blue}{\tan z}\right) - 1\right)}{\tan y + \tan z}} - \tan a\right) \]

8. Applied egg-rr 99.7%

   \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\left(\left(1 + \tan y \cdot \tan z\right) - 1\right)}}{\tan y + \tan z}} - \tan a\right) \]
9. Step-by-step derivation

   1. associate--l+ 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\left(1 + \left(\tan y \cdot \tan z - 1\right)\right)}}{\tan y + \tan z}} - \tan a\right) \]

   2. fmm-def 99.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(1 + \color{blue}{\mathsf{fma}\left(\tan y, \tan z, -1\right)}\right)}{\tan y + \tan z}} - \tan a\right) \]

   3. metadata-eval 99.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(1 + \mathsf{fma}\left(\tan y, \tan z, \color{blue}{-1}\right)\right)}{\tan y + \tan z}} - \tan a\right) \]

10. Simplified 99.8%

    \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\left(1 + \mathsf{fma}\left(\tan y, \tan z, -1\right)\right)}}{\tan y + \tan z}} - \tan a\right) \]
11. Step-by-step derivation

    1. associate-+r- 99.7%

       \[\leadsto \color{blue}{\left(x + \frac{1}{\frac{1 - \left(1 + \mathsf{fma}\left(\tan y, \tan z, -1\right)\right)}{\tan y + \tan z}}\right) - \tan a} \]

    2. associate-/r/ 99.7%

       \[\leadsto \left(x + \color{blue}{\frac{1}{1 - \left(1 + \mathsf{fma}\left(\tan y, \tan z, -1\right)\right)} \cdot \left(\tan y + \tan z\right)}\right) - \tan a \]

    3. associate--r+ 99.7%

       \[\leadsto \left(x + \frac{1}{\color{blue}{\left(1 - 1\right) - \mathsf{fma}\left(\tan y, \tan z, -1\right)}} \cdot \left(\tan y + \tan z\right)\right) - \tan a \]

    4. metadata-eval 99.7%

       \[\leadsto \left(x + \frac{1}{\color{blue}{0} - \mathsf{fma}\left(\tan y, \tan z, -1\right)} \cdot \left(\tan y + \tan z\right)\right) - \tan a \]

12. Applied egg-rr 99.7%

    \[\leadsto \color{blue}{\left(x + \frac{1}{0 - \mathsf{fma}\left(\tan y, \tan z, -1\right)} \cdot \left(\tan y + \tan z\right)\right) - \tan a} \]
13. Step-by-step derivation

    1. associate-+r- 99.7%

       \[\leadsto \color{blue}{x + \left(\frac{1}{0 - \mathsf{fma}\left(\tan y, \tan z, -1\right)} \cdot \left(\tan y + \tan z\right) - \tan a\right)} \]

    2. associate-*l/ 99.8%

       \[\leadsto x + \left(\color{blue}{\frac{1 \cdot \left(\tan y + \tan z\right)}{0 - \mathsf{fma}\left(\tan y, \tan z, -1\right)}} - \tan a\right) \]

    3. *-lft-identity 99.8%

       \[\leadsto x + \left(\frac{\color{blue}{\tan y + \tan z}}{0 - \mathsf{fma}\left(\tan y, \tan z, -1\right)} - \tan a\right) \]

    4. sub0-neg 99.8%

       \[\leadsto x + \left(\frac{\tan y + \tan z}{\color{blue}{-\mathsf{fma}\left(\tan y, \tan z, -1\right)}} - \tan a\right) \]

14. Simplified 99.8%

    \[\leadsto \color{blue}{x + \left(\frac{\tan y + \tan z}{-\mathsf{fma}\left(\tan y, \tan z, -1\right)} - \tan a\right)} \]

15. Final simplification 99.8%

    \[\leadsto x - \left(\tan a + \frac{\tan y + \tan z}{\mathsf{fma}\left(\tan y, \tan z, -1\right)}\right) \]
16. Add Preprocessing

Alternative 4: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\frac{1}{\frac{1 + \left(1 + \left(-1 - \tan y \cdot \tan z\right)\right)}{\tan y + \tan z}} - \tan a\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+
  x
  (-
   (/ 1.0 (/ (+ 1.0 (+ 1.0 (- -1.0 (* (tan y) (tan z))))) (+ (tan y) (tan z))))
   (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + ((1.0 / ((1.0 + (1.0 + (-1.0 - (tan(y) * tan(z))))) / (tan(y) + tan(z)))) - tan(a));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + ((1.0d0 / ((1.0d0 + (1.0d0 + ((-1.0d0) - (tan(y) * tan(z))))) / (tan(y) + tan(z)))) - tan(a))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + ((1.0 / ((1.0 + (1.0 + (-1.0 - (Math.tan(y) * Math.tan(z))))) / (Math.tan(y) + Math.tan(z)))) - Math.tan(a));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + ((1.0 / ((1.0 + (1.0 + (-1.0 - (math.tan(y) * math.tan(z))))) / (math.tan(y) + math.tan(z)))) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 + Float64(1.0 + Float64(-1.0 - Float64(tan(y) * tan(z))))) / Float64(tan(y) + tan(z)))) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + ((1.0 / ((1.0 + (1.0 + (-1.0 - (tan(y) * tan(z))))) / (tan(y) + tan(z)))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(1.0 / N[(N[(1.0 + N[(1.0 + N[(-1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.2%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. clear-num 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

4. Applied egg-rr 99.7%

   \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]
5. Step-by-step derivation

   1. expm1-log1p-u 90.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan y \cdot \tan z\right)\right)}}{\tan y + \tan z}} - \tan a\right) \]

   2. expm1-undefine 90.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\tan y \cdot \tan z\right)} - 1\right)}}{\tan y + \tan z}} - \tan a\right) \]

   3. log1p-undefine 90.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(e^{\color{blue}{\log \left(1 + \tan y \cdot \tan z\right)}} - 1\right)}{\tan y + \tan z}} - \tan a\right) \]

   4. add-exp-log 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(\color{blue}{\left(1 + \tan y \cdot \tan z\right)} - 1\right)}{\tan y + \tan z}} - \tan a\right) \]

   5. +-commutative 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \left(\color{blue}{\left(\tan y \cdot \tan z + 1\right)} - 1\right)}{\tan y + \tan z}} - \tan a\right) \]

6. Applied egg-rr 99.7%

   \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\left(\left(\tan y \cdot \tan z + 1\right) - 1\right)}}{\tan y + \tan z}} - \tan a\right) \]

7. Final simplification 99.7%

   \[\leadsto x + \left(\frac{1}{\frac{1 + \left(1 + \left(-1 - \tan y \cdot \tan z\right)\right)}{\tan y + \tan z}} - \tan a\right) \]
8. Add Preprocessing

Alternative 5: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}} - \tan a\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+ x (- (/ 1.0 (/ (- 1.0 (* (tan y) (tan z))) (+ (tan y) (tan z)))) (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + ((1.0 / ((1.0 - (tan(y) * tan(z))) / (tan(y) + tan(z)))) - tan(a));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + ((1.0d0 / ((1.0d0 - (tan(y) * tan(z))) / (tan(y) + tan(z)))) - tan(a))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + ((1.0 / ((1.0 - (Math.tan(y) * Math.tan(z))) / (Math.tan(y) + Math.tan(z)))) - Math.tan(a));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + ((1.0 / ((1.0 - (math.tan(y) * math.tan(z))) / (math.tan(y) + math.tan(z)))) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 - Float64(tan(y) * tan(z))) / Float64(tan(y) + tan(z)))) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + ((1.0 / ((1.0 - (tan(y) * tan(z))) / (tan(y) + tan(z)))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(1.0 / N[(N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.2%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. clear-num 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

4. Applied egg-rr 99.7%

   \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]
5. Add Preprocessing

Alternative 6: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+ x (- (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - tan(a));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) - tan(a))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + (((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) - Math.tan(a));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + (((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.2%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 77.2%

      \[\leadsto \color{blue}{\left(\tan \left(y + z\right) - \tan a\right) + x} \]

   2. sub-neg 77.2%

      \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + \left(-\tan a\right)\right)} + x \]

   3. associate-+l+ 77.2%

      \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(\left(-\tan a\right) + x\right)} \]

   4. tan-sum 99.6%

      \[\leadsto \color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} + \left(\left(-\tan a\right) + x\right) \]

   5. div-inv 99.6%

      \[\leadsto \color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} + \left(\left(-\tan a\right) + x\right) \]

   6. fma-define 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\tan y + \tan z, \frac{1}{1 - \tan y \cdot \tan z}, \left(-\tan a\right) + x\right)} \]

   7. neg-mul-1 99.6%

      \[\leadsto \mathsf{fma}\left(\tan y + \tan z, \frac{1}{1 - \tan y \cdot \tan z}, \color{blue}{-1 \cdot \tan a} + x\right) \]

   8. fma-define 99.6%

      \[\leadsto \mathsf{fma}\left(\tan y + \tan z, \frac{1}{1 - \tan y \cdot \tan z}, \color{blue}{\mathsf{fma}\left(-1, \tan a, x\right)}\right) \]

4. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\tan y + \tan z, \frac{1}{1 - \tan y \cdot \tan z}, \mathsf{fma}\left(-1, \tan a, x\right)\right)} \]
5. Step-by-step derivation

   1. fma-undefine 99.6%

      \[\leadsto \color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z} + \mathsf{fma}\left(-1, \tan a, x\right)} \]

   2. fma-undefine 99.6%

      \[\leadsto \left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z} + \color{blue}{\left(-1 \cdot \tan a + x\right)} \]

   3. neg-mul-1 99.6%

      \[\leadsto \left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z} + \left(\color{blue}{\left(-\tan a\right)} + x\right) \]

   4. associate-+r+ 99.7%

      \[\leadsto \color{blue}{\left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z} + \left(-\tan a\right)\right) + x} \]

   5. sub-neg 99.7%

      \[\leadsto \color{blue}{\left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z} - \tan a\right)} + x \]

   6. associate-*r/ 99.7%

      \[\leadsto \left(\color{blue}{\frac{\left(\tan y + \tan z\right) \cdot 1}{1 - \tan y \cdot \tan z}} - \tan a\right) + x \]

   7. *-rgt-identity 99.7%

      \[\leadsto \left(\frac{\color{blue}{\tan y + \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right) + x \]

6. Simplified 99.7%

   \[\leadsto \color{blue}{\left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right) + x} \]

7. Final simplification 99.7%

   \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right) \]
8. Add Preprocessing

Alternative 7: 89.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;a \leq -2.6 \lor \neg \left(a \leq 0.0275\right):\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{t\_0}} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1 - \tan y \cdot \tan z}{t\_0}} - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (or (<= a -2.6) (not (<= a 0.0275)))
     (+ x (- (/ 1.0 (/ 1.0 t_0)) (tan a)))
     (+ x (- (/ 1.0 (/ (- 1.0 (* (tan y) (tan z))) t_0)) a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if ((a <= -2.6) || !(a <= 0.0275)) {
		tmp = x + ((1.0 / (1.0 / t_0)) - tan(a));
	} else {
		tmp = x + ((1.0 / ((1.0 - (tan(y) * tan(z))) / t_0)) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: t_0
    real(8) :: tmp
    t_0 = tan(y) + tan(z)
    if ((a <= (-2.6d0)) .or. (.not. (a <= 0.0275d0))) then
        tmp = x + ((1.0d0 / (1.0d0 / t_0)) - tan(a))
    else
        tmp = x + ((1.0d0 / ((1.0d0 - (tan(y) * tan(z))) / t_0)) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double t_0 = Math.tan(y) + Math.tan(z);
	double tmp;
	if ((a <= -2.6) || !(a <= 0.0275)) {
		tmp = x + ((1.0 / (1.0 / t_0)) - Math.tan(a));
	} else {
		tmp = x + ((1.0 / ((1.0 - (Math.tan(y) * Math.tan(z))) / t_0)) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = math.tan(y) + math.tan(z)
	tmp = 0
	if (a <= -2.6) or not (a <= 0.0275):
		tmp = x + ((1.0 / (1.0 / t_0)) - math.tan(a))
	else:
		tmp = x + ((1.0 / ((1.0 - (math.tan(y) * math.tan(z))) / t_0)) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if ((a <= -2.6) || !(a <= 0.0275))
		tmp = Float64(x + Float64(Float64(1.0 / Float64(1.0 / t_0)) - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 - Float64(tan(y) * tan(z))) / t_0)) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	t_0 = tan(y) + tan(z);
	tmp = 0.0;
	if ((a <= -2.6) || ~((a <= 0.0275)))
		tmp = x + ((1.0 / (1.0 / t_0)) - tan(a));
	else
		tmp = x + ((1.0 / ((1.0 - (tan(y) * tan(z))) / t_0)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -2.6], N[Not[LessEqual[a, 0.0275]], $MachinePrecision]], N[(x + N[(N[(1.0 / N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / N[(N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.60000000000000009 or 0.0275000000000000001 < a

   1. Initial program 76.5%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. tan-sum 99.7%

         \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

      2. clear-num 99.7%

         \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]
   5. Step-by-step derivation

      1. tan-quot 99.7%

         \[\leadsto x + \left(\frac{1}{\frac{1 - \tan y \cdot \color{blue}{\frac{\sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

      2. associate-*r/ 99.8%

         \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

   7. Taylor expanded in y around 0 77.7%

      \[\leadsto x + \left(\frac{1}{\frac{\color{blue}{1}}{\tan y + \tan z}} - \tan a\right) \]

   if -2.60000000000000009 < a < 0.0275000000000000001

   1. Initial program 77.9%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 78.0%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]
   4. Step-by-step derivation

      1. tan-sum 99.7%

         \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

      2. clear-num 99.7%

         \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

   5. Applied egg-rr 98.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - a\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \lor \neg \left(a \leq 0.0275\right):\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan y + \tan z}} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;a \leq -2.6 \lor \neg \left(a \leq 0.0275\right):\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{t\_0}} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{t\_0}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (or (<= a -2.6) (not (<= a 0.0275)))
     (+ x (- (/ 1.0 (/ 1.0 t_0)) (tan a)))
     (+ x (- (/ t_0 (- 1.0 (* (tan y) (tan z)))) a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if ((a <= -2.6) || !(a <= 0.0275)) {
		tmp = x + ((1.0 / (1.0 / t_0)) - tan(a));
	} else {
		tmp = x + ((t_0 / (1.0 - (tan(y) * tan(z)))) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: t_0
    real(8) :: tmp
    t_0 = tan(y) + tan(z)
    if ((a <= (-2.6d0)) .or. (.not. (a <= 0.0275d0))) then
        tmp = x + ((1.0d0 / (1.0d0 / t_0)) - tan(a))
    else
        tmp = x + ((t_0 / (1.0d0 - (tan(y) * tan(z)))) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double t_0 = Math.tan(y) + Math.tan(z);
	double tmp;
	if ((a <= -2.6) || !(a <= 0.0275)) {
		tmp = x + ((1.0 / (1.0 / t_0)) - Math.tan(a));
	} else {
		tmp = x + ((t_0 / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = math.tan(y) + math.tan(z)
	tmp = 0
	if (a <= -2.6) or not (a <= 0.0275):
		tmp = x + ((1.0 / (1.0 / t_0)) - math.tan(a))
	else:
		tmp = x + ((t_0 / (1.0 - (math.tan(y) * math.tan(z)))) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if ((a <= -2.6) || !(a <= 0.0275))
		tmp = Float64(x + Float64(Float64(1.0 / Float64(1.0 / t_0)) - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(t_0 / Float64(1.0 - Float64(tan(y) * tan(z)))) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	t_0 = tan(y) + tan(z);
	tmp = 0.0;
	if ((a <= -2.6) || ~((a <= 0.0275)))
		tmp = x + ((1.0 / (1.0 / t_0)) - tan(a));
	else
		tmp = x + ((t_0 / (1.0 - (tan(y) * tan(z)))) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -2.6], N[Not[LessEqual[a, 0.0275]], $MachinePrecision]], N[(x + N[(N[(1.0 / N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t$95$0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.60000000000000009 or 0.0275000000000000001 < a

   1. Initial program 76.5%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. tan-sum 99.7%

         \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

      2. clear-num 99.7%

         \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]
   5. Step-by-step derivation

      1. tan-quot 99.7%

         \[\leadsto x + \left(\frac{1}{\frac{1 - \tan y \cdot \color{blue}{\frac{\sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

      2. associate-*r/ 99.8%

         \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

   7. Taylor expanded in y around 0 77.7%

      \[\leadsto x + \left(\frac{1}{\frac{\color{blue}{1}}{\tan y + \tan z}} - \tan a\right) \]

   if -2.60000000000000009 < a < 0.0275000000000000001

   1. Initial program 77.9%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 78.0%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]
   4. Step-by-step derivation

      1. tan-sum 98.7%

         \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - a\right) \]

      2. div-inv 98.7%

         \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - a\right) \]

   5. Applied egg-rr 98.7%

      \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - a\right) \]
   6. Step-by-step derivation

      1. associate-*r/ 98.7%

         \[\leadsto x + \left(\color{blue}{\frac{\left(\tan y + \tan z\right) \cdot 1}{1 - \tan y \cdot \tan z}} - a\right) \]

      2. *-rgt-identity 98.7%

         \[\leadsto x + \left(\frac{\color{blue}{\tan y + \tan z}}{1 - \tan y \cdot \tan z} - a\right) \]

   7. Simplified 98.7%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - a\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \lor \neg \left(a \leq 0.0275\right):\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan y + \tan z}} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\frac{1}{\frac{1}{\tan y + \tan z}} - \tan a\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+ x (- (/ 1.0 (/ 1.0 (+ (tan y) (tan z)))) (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + ((1.0 / (1.0 / (tan(y) + tan(z)))) - tan(a));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + ((1.0d0 / (1.0d0 / (tan(y) + tan(z)))) - tan(a))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + ((1.0 / (1.0 / (Math.tan(y) + Math.tan(z)))) - Math.tan(a));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + ((1.0 / (1.0 / (math.tan(y) + math.tan(z)))) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(Float64(1.0 / Float64(1.0 / Float64(tan(y) + tan(z)))) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + ((1.0 / (1.0 / (tan(y) + tan(z)))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(1.0 / N[(1.0 / N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.2%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. clear-num 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

4. Applied egg-rr 99.7%

   \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]
5. Step-by-step derivation

   1. tan-quot 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \tan y \cdot \color{blue}{\frac{\sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

   2. associate-*r/ 99.7%

      \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

6. Applied egg-rr 99.7%

   \[\leadsto x + \left(\frac{1}{\frac{1 - \color{blue}{\frac{\tan y \cdot \sin z}{\cos z}}}{\tan y + \tan z}} - \tan a\right) \]

7. Taylor expanded in y around 0 77.9%

   \[\leadsto x + \left(\frac{1}{\frac{\color{blue}{1}}{\tan y + \tan z}} - \tan a\right) \]
8. Add Preprocessing

Alternative 10: 79.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\tan \left(y + z\right) - \frac{\sin a}{\cos a}\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+ x (- (tan (+ y z)) (/ (sin a) (cos a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - (sin(a) / cos(a)));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - (sin(a) / cos(a)))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - (Math.sin(a) / Math.cos(a)));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + (math.tan((y + z)) - (math.sin(a) / math.cos(a)))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - Float64(sin(a) / cos(a))))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - (sin(a) / cos(a)));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[(N[Sin[a], $MachinePrecision] / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.2%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 77.2%

   \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{\frac{\sin a}{\cos a}}\right) \]
4. Add Preprocessing

Alternative 11: 69.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \lor \neg \left(a \leq 0.0022\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -2.6) (not (<= a 0.0022)))
   (+ x (- (tan y) (tan a)))
   (+ x (- (tan (+ y z)) a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.6) || !(a <= 0.0022)) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = x + (tan((y + z)) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.6d0)) .or. (.not. (a <= 0.0022d0))) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = x + (tan((y + z)) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.6) || !(a <= 0.0022)) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (a <= -2.6) or not (a <= 0.0022):
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -2.6) || !(a <= 0.0022))
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -2.6) || ~((a <= 0.0022)))
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[a, -2.6], N[Not[LessEqual[a, 0.0022]], $MachinePrecision]], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.60000000000000009 or 0.00220000000000000013 < a

   1. Initial program 76.0%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.2%

      \[\leadsto x + \left(\tan \color{blue}{y} - \tan a\right) \]

   if -2.60000000000000009 < a < 0.00220000000000000013

   1. Initial program 78.3%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 78.4%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \lor \neg \left(a \leq 0.0022\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= y -7.5e-6) (+ x (- (tan y) (tan a))) (+ x (- (tan z) (tan a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -7.5e-6) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = x + (tan(z) - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-7.5d-6)) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = x + (tan(z) - tan(a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -7.5e-6) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if y <= -7.5e-6:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (y <= -7.5e-6)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -7.5e-6)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[y, -7.5e-6], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000019e-6

   1. Initial program 63.1%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 63.6%

      \[\leadsto x + \left(\tan \color{blue}{y} - \tan a\right) \]

   if -7.50000000000000019e-6 < y

   1. Initial program 81.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.5%

      \[\leadsto x + \left(\tan \color{blue}{z} - \tan a\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.2%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 14: 56.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -23 \lor \neg \left(a \leq 0.3\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -23.0) (not (<= a 0.3)))
   (+ x (- z (tan a)))
   (+ x (- (tan (+ y z)) a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -23.0) || !(a <= 0.3)) {
		tmp = x + (z - tan(a));
	} else {
		tmp = x + (tan((y + z)) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-23.0d0)) .or. (.not. (a <= 0.3d0))) then
        tmp = x + (z - tan(a))
    else
        tmp = x + (tan((y + z)) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -23.0) || !(a <= 0.3)) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (a <= -23.0) or not (a <= 0.3):
		tmp = x + (z - math.tan(a))
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -23.0) || !(a <= 0.3))
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -23.0) || ~((a <= 0.3)))
		tmp = x + (z - tan(a));
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[a, -23.0], N[Not[LessEqual[a, 0.3]], $MachinePrecision]], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -23 or 0.299999999999999989 < a

   1. Initial program 76.3%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 61.1%

      \[\leadsto x + \left(\color{blue}{\frac{\sin z}{\cos z}} - \tan a\right) \]

   4. Taylor expanded in z around 0 33.1%

      \[\leadsto x + \left(\color{blue}{z} - \tan a\right) \]

   if -23 < a < 0.299999999999999989

   1. Initial program 78.1%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 77.6%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -23 \lor \neg \left(a \leq 0.3\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \lor \neg \left(a \leq 0.175\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -2.6) (not (<= a 0.175)))
   (+ x (- z (tan a)))
   (+ x (- (tan y) a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.6) || !(a <= 0.175)) {
		tmp = x + (z - tan(a));
	} else {
		tmp = x + (tan(y) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.6d0)) .or. (.not. (a <= 0.175d0))) then
        tmp = x + (z - tan(a))
    else
        tmp = x + (tan(y) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.6) || !(a <= 0.175)) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x + (Math.tan(y) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (a <= -2.6) or not (a <= 0.175):
		tmp = x + (z - math.tan(a))
	else:
		tmp = x + (math.tan(y) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -2.6) || !(a <= 0.175))
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = Float64(x + Float64(tan(y) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -2.6) || ~((a <= 0.175)))
		tmp = x + (z - tan(a));
	else
		tmp = x + (tan(y) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[a, -2.6], N[Not[LessEqual[a, 0.175]], $MachinePrecision]], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[y], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.60000000000000009 or 0.17499999999999999 < a

   1. Initial program 76.3%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 61.1%

      \[\leadsto x + \left(\color{blue}{\frac{\sin z}{\cos z}} - \tan a\right) \]

   4. Taylor expanded in z around 0 33.1%

      \[\leadsto x + \left(\color{blue}{z} - \tan a\right) \]

   if -2.60000000000000009 < a < 0.17499999999999999

   1. Initial program 78.1%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 77.6%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]

   4. Taylor expanded in y around inf 60.4%

      \[\leadsto x + \left(\tan \color{blue}{y} - a\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \lor \neg \left(a \leq 0.175\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-221}:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \mathbf{elif}\;z \leq 580:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= z -2.4e-221)
   (+ x (- (tan y) a))
   (if (<= z 580.0) (+ x (- z (tan a))) (+ x (- (tan z) a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= -2.4e-221) {
		tmp = x + (tan(y) - a);
	} else if (z <= 580.0) {
		tmp = x + (z - tan(a));
	} else {
		tmp = x + (tan(z) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.4d-221)) then
        tmp = x + (tan(y) - a)
    else if (z <= 580.0d0) then
        tmp = x + (z - tan(a))
    else
        tmp = x + (tan(z) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= -2.4e-221) {
		tmp = x + (Math.tan(y) - a);
	} else if (z <= 580.0) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x + (Math.tan(z) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if z <= -2.4e-221:
		tmp = x + (math.tan(y) - a)
	elif z <= 580.0:
		tmp = x + (z - math.tan(a))
	else:
		tmp = x + (math.tan(z) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (z <= -2.4e-221)
		tmp = Float64(x + Float64(tan(y) - a));
	elseif (z <= 580.0)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = Float64(x + Float64(tan(z) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (z <= -2.4e-221)
		tmp = x + (tan(y) - a);
	elseif (z <= 580.0)
		tmp = x + (z - tan(a));
	else
		tmp = x + (tan(z) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[z, -2.4e-221], N[(x + N[(N[Tan[y], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 580.0], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.40000000000000024e-221

   1. Initial program 71.6%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 39.7%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]

   4. Taylor expanded in y around inf 30.6%

      \[\leadsto x + \left(\tan \color{blue}{y} - a\right) \]

   if -2.40000000000000024e-221 < z < 580

   1. Initial program 99.9%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 63.0%

      \[\leadsto x + \left(\color{blue}{\frac{\sin z}{\cos z}} - \tan a\right) \]

   4. Taylor expanded in z around 0 63.0%

      \[\leadsto x + \left(\color{blue}{z} - \tan a\right) \]

   if 580 < z

   1. Initial program 56.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 34.7%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]

   4. Taylor expanded in y around 0 34.5%

      \[\leadsto x + \left(\tan \color{blue}{z} - a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 40.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.4:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 (if (<= z 1.4) (+ x (- z (tan a))) x))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 1.4) {
		tmp = x + (z - tan(a));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= 1.4d0) then
        tmp = x + (z - tan(a))
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 1.4) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if z <= 1.4:
		tmp = x + (z - math.tan(a))
	else:
		tmp = x
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (z <= 1.4)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (z <= 1.4)
		tmp = x + (z - tan(a));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[z, 1.4], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < 1.3999999999999999

   1. Initial program 83.1%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 58.1%

      \[\leadsto x + \left(\color{blue}{\frac{\sin z}{\cos z}} - \tan a\right) \]

   4. Taylor expanded in z around 0 38.3%

      \[\leadsto x + \left(\color{blue}{z} - \tan a\right) \]

   if 1.3999999999999999 < z

   1. Initial program 56.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 21.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 31.8% accurate, 207.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 x)

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return x
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := x

Derivation

1. Initial program 77.2%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf 30.9%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024180 
(FPCore (x y z a)
  :name "tan-example (used to crash)"
  :precision binary64
  :pre (and (and (and (or (== x 0.0) (and (<= 0.5884142 x) (<= x 505.5909))) (or (and (<= -1.796658e+308 y) (<= y -9.425585e-310)) (and (<= 1.284938e-309 y) (<= y 1.751224e+308)))) (or (and (<= -1.776707e+308 z) (<= z -8.599796e-310)) (and (<= 3.293145e-311 z) (<= z 1.725154e+308)))) (or (and (<= -1.796658e+308 a) (<= a -9.425585e-310)) (and (<= 1.284938e-309 a) (<= a 1.751224e+308))))
  (+ x (- (tan (+ y z)) (tan a))))